2.2.4 \(u_{tt} - 2 u_{xt} - 3 u_{xx} = 0\) with \(u(0,x)=x^2, u_t(x,0)=e^x\)

problem number 82

Added Oct 6, 2019.

Problem 2.4.19 Peter Olver, Into to Partial differential equations 4th edition

Solve \(u_{tt} - 2 u_{xt} - 3 u_{xx} = 0\) with \(u(0,x)=x^2, u_t(x,0)=e^x\)

Mathematica


\[\left \{\left \{u(x,t)\to 3 t^2-\frac {e^{x-t}}{4}+\frac {1}{4} e^{3 t+x}+x^2\right \}\right \}\]

Maple


\[u \left (x , t\right ) = x^{2}+{\mathrm e}^{x}-{\mathrm e}^{-t +x}\]